Final Exam Study Guide for Math 1322, Fall 99

Review:

• The covered material in the text.
• The three exams
• The quizzes
• The homework

There will be no questions on Matlab on the exam.

Topics to concentrate on:

• Main definitions and theorems: Riemann integral, the fundamental theorem of calculus (both parts), radius of convergence of a power series.
• Integration by elementary substitutions.
• Integration by parts.
• Total Change Theorem, p.377. For example, given velocity, how far does a particle travel in a given interval of time?
• Area between curves. Be able to sketch the region so that you can tell which curve is on top, or to the right.
• Volumes of solids of revolution, or other solids for which you can find the cross sectional areas. Planar or cylindrical cross section methods.
• Area of regions enclosed by curves defined parametrically. Remember Area is the integral from x=a to x=b of ydx, then make the substitutions.
• Probability density functions and their integrals over [a,b] interpreted as a probability. The normal probability density functions.
• Work problems: to pull a leaky bucket of water out of a well, to pump liquid out of a tank, to pull a cable to the top of a building, etc.
• What are separable differential equations? Know how to solve them.
• Know how to verify if a given function is a solution of a differential equation. Initial conditions.
• Mixing problems. One of these is highly likely because one did not appear on a midterm exam or quiz. See the one you did on the homework.
• Convergence tests for series: know geometric series and p-series, comparison test, integral test, alternating series test, ratio test. What does absolute convergence mean?
• Sum of a geometric series.
• The Maclaurin series of sin(x), cos(x), exp(x), arctan(x), ln(1+x) and easy variations on these, such as exp(-x) and sin x².
• Power series. Understand the meaning of the radius of convergence.
• Find the radius of convergence of a power series using the ratio test. Find the interval of convergence of a power series.
• Maclaurin and Taylor series, Taylor polynomial of a given degree.
• Taylor's Remainder Estimate.